Omega Phase Transformation Research Articles

Effect of hydrostatic pressure on the kinetics of alpha–omega phase transformation in zirconium

A three dimensional (3D) elastoplastic phase-field model, including strain hardening, is employed to study the effect of hydrostatic pressure in the range of 4–9 GPa on the kinetics of alpha–omega phase transformation in zirconium (Zr). The input data corresponding to pure Zr are acquired from experimental studies as well as by using the CALPHAD method. A decreasing incubation time, for the formation of omega variants, with increasing pressure is observed. Avrami (JMAK) equation is used to study the transformation kinetics by analysing the phase fraction plots predicted by the phase-field simulations. The estimated activation energy is in the range of 54–59 kJ mol−1 and decreases at an average rate of 992 J mol−1 per 1 GPa increase in pressure. The analysis of Avrami exponents, based on Cahn’s approach, show that the transformation region can be divided into two distinct regions with a change in slope, which is attributed to the site saturation. It is concluded that in the first region where the exponents are above 3, the transformation proceeds by nucleation and growth. In the second region where the exponents are sub-unity, the transformation proceeds by growth of the existing variants.

Tensile behavior of dual-phase titanium alloys under high-intensity proton beam exposure: Radiation-induced omega phase transformation in Ti-6Al-4V

A high-intensity proton beam exposure with 181 MeV energy has been conducted at Brookhaven Linac Isotope Producer facility on various material specimens for accelerator targetry applications, including titanium alloys as a beam window material. The radiation damage level of the analyzed capsule was 0.25 dpa at beam center region with an irradiation temperature around 120 °C. Tensile tests showed increased hardness and a large decrease in ductility for the dual α+β-phase Ti-6Al-4V Grade-5 and Grade-23 extra low interstitial alloys, with the near α-phase Ti-3Al-2.5V Grade-9 alloy still exhibiting uniform elongation of a few % after irradiation. Transmission Electron Microscope analyses on Ti-6Al-4V indicated clear evidence of a high-density of defect clusters with size less than 2 nm in each α-phase grain. The β-phase grains did not contain any visible defects such as loops or black dots, while the diffraction patterns clearly indicated ω-phase precipitation in an advanced formation stage. The radiation-induced ω-phase transformation in the β-phase could lead to greater loss of ductility in Ti-6Al-4V alloys in comparison with Ti-3Al-2.5V alloy with less β-phase.

Role of twinning on the omega-phase transformation and stability in zirconium

Group-IV transition metal zirconium is used in nuclear and chemical industries as a choice material for operating in extreme environments. At ambient-conditions, zirconium has a stable hexagonal-close-packed structure (α-phase), but under high-pressures it transforms into a simple-hexagonal structure (ω-phase). Experimental studies involving high-pressures have reported retention of ω-phase upon recovery to ambient-pressures, which is undesirable since the ω-phase is brittle compared to the α-phase. Understanding the α-to-ω transformation is relevant for enhancing the applicability of transition metals. In this work using in-situ synchrotron X-ray diffraction, we show that deformation twins in the α-phase lower the transformation pressure and increase the amount of retained ω-phase. Our analysis concludes that the characteristics of the stress fields associated with the twins promote the α-to-ω transformation while making the reverse transformation energetically unfavorable. This work reveals a plausible way to design Zr microstructure for high-pressure applications via controlling twinning and retained ω-phase.

Mechanical (Compressive) Form of Driving Force Triggered the Phase Transformation from Beta to Omega & Alpha Phases by Means of Dislocation Slips in Metastable Beta Phase Field Ti-5553 Alloy

Most of structural alloys' applications are under static, dynamic and cyclic forms of loading, for which Ti-5553 alloy in beta phase field is being investigated to confirm the mechanism of deformation and phase transformation upon quasi-static and dynamic compression. To achieve the fully beta phase field, Ti-5553 alloy was heated at 900oC (almost 50oC above beta tarsus temp.) for one hour of soaking time followed by air quenching. Thereafter, Dynamic compression (DC) by Split Hopkinson Pressure Bar (SHPB) and Quasi-static compression (QSC) were performed at strain rate of 103/s and 10-3/s, respectively. Recovered specimens were thoroughly examined by using different tools such as OM, SEM, HRTEM, EBSD to get reliable data for justification of logical conclusions. It's found that the prominent mode of deformation was dislocation slips along with twining to some extent in both of QSC and DC but sliding and spalling of grain boundary was more noticeable in former. Transformation of phases occurred in saturated dislocation slips grains in which from beta (BCC) to omega transformation has been completed by mechanical form of driving force in a way when set of two adjacent (110)ᵦ planes covered ±1/6 of total separation distance between two next to each other (111)ᵦ planes, equal but opposite shears, in (111)ᵦ direction and it could be justified by the 3% shrinkage of two closely existed (110)ᵦ planes after transformation to omega. Furthermore, it is noticed that the omega phase and alpha transformation occurred in the grains which were saturated with dislocation slips.

Coupled strain-induced alpha to omega phase transformation and plastic flow in zirconium under high pressure torsion in a rotational diamond anvil cell

Strain-induced α→ω phase transformation (PT) in the zirconium (Zr) sample under compression and plastic shear in a rotational diamond anvil cell (RDAC) is investigated using the finite element method (FEM). The fields of the volume fraction of the ω phase, all components of the stress tensor, and plastic strain are presented. Before torsion, PT barely occurs. During torsion under a fixed applied force, PT initiates at the center of the sample, where the pressure first reaches the minimum pressure for strain-induced α→ω PT,pεd, and propagates from the center to the periphery and from the symmetry plane to the contact surface. Salient increase of the shear friction stress and pressure at the center of a sample, so-called pressure self-multiplication effect observed experimentally for some other materials, is predicted here for Zr. It is caused by much higher yield strength of the ω phase in comparison with the α phase. Except at the very center of a sample, the total contact friction stress is equal to the yield strength in shear of the mixture of phases and the plastic sliding occurs there. Due to the reduction in sample thickness and radial material flow during torsion, the ω phase can be observed in the region where pressure is lower than pεd, which may lead to misinterpretation of the experimental data for pεd. For the same applied force, torsion drastically promotes PT in comparison with the compression without torsion. However, the PT process in RDAC is far from optimal: (a) due to the pressure self-multiplication effect, the pressure in the transformed region is much higher than that required for PT; (b) the region in which PT occurs is limited by the pressure pεd and cannot be expanded by increasing a shear under a fixed force; and (c) the significant reduction in thickness during torsion reduces the total mass of the high-pressure phase. These drawbacks can be overcome by placing a sample within a strong gasket with an optimized geometry. It is shown that, due to strong pressure heterogeneity, characterization of α→ω and α→β PTs based on the averaged pressure contains large errors. The obtained results, in addition to providing an improved understanding of the strain-induced PTs, may be beneficial for the optimum design of experiments and the extraction of material parameters, as well as optimization and control of PTs by varying the geometry and loading conditions.

Plastic flows and strain-induced alpha to omega phase transformation in zirconium during compression in a diamond anvil cell: Finite element simulations

Coupled plastic flows and the strain-induced α→ω phase transformation (PT) in a zirconium sample under compression in a diamond anvil cell are investigated using finite element method (FEM). The PT is treated as strain-induced rather than pressure-induced and the previously developed model for strain-induced PTs is utilized. Very heterogeneous fields of stress tensor, accumulated plastic strain, and concentration of the ω phase are obtained for different applied loads. The PT starts at the center of a sample when pressure exceeds the minimum pressurepεd=1.7GPa, below which a direct strain-induced PT to a high pressure phase cannot occur, and it propagates from the center to the periphery with an increasing load. Even at the maximum pressure of 7GPa, the PT is not completed everywhere. With an increasing load, the pressure and pressure gradient along the radial direction significantly increase in the two-phase region due to the much larger yield strength of the ω phase. This in turn promotes transformation and produces a positive mechanochemical feedback. Obtained results are utilized for the interpretation of published experimental data on pressure-, stress-, and strain-induced α→ω PTs in Zr and Titanium (Ti) and α→β and ω→β PTs in Zr under compression and high pressure torsion. This includes correcting the reported minimum pressures for these transformations by a factor of 3–6 due to the stress heterogeneity, the effect of transmitting media, the pressure hysteresis, and the reversibility of the transformation.

Anisotropic kinetics of solid phase transition from first principles: alpha-omega phase transformation of Zr.

Structural inhomogeneity is ubiquitous in solid crystals and plays critical roles in phase nucleation and propagation. Here, we develop a heterogeneous solid-solid phase transition theory for predicting the prevailing heterophase junctions, the metastable states governing microstructure evolution in solids. Using this theory and first-principles pathway sampling simulation, we determine two types of heterophase junctions pertaining to metal α-ω phase transition at different pressures and predict the reversibility of transformation only at low pressures, i.e. below 7 GPa. The low-pressure transformation is dominated by displacive Martensitic mechanism, while the high-pressure one is controlled by the reconstructive mechanism. The mechanism of α-ω phase transition is thus highly pressure-sensitive, for which the traditional homogeneous model fails to explain the experimental observations. The results provide the first atomic-level evidence on the coexistence of two different solid phase transition mechanisms in one system.

Alpha – omega and omega – alpha phase transformations in zirconium under hydrostatic pressure: A 3D mesoscale study

A three dimensional (3D) elastoplastic phase-field model is developed for modeling the hydrostatic pressure-induced alpha – omega phase transformation and the reverse phase transformation, i.e. omega – alpha, in zirconium (Zr). Plastic deformation and strain hardening of the material are also considered in the model. The microstructure evolution during both phase transformations is studied. The transformation start pressures at different temperatures are predicted and are plotted as a phase diagram. The effect of phase transformations on the mechanical properties of the material is also studied. The input data corresponding to pure Zr are acquired from experimental studies as well as by using the CALPHAD method. Our simulations show that three different omega variants form as laths. On release of pressure, reverse phase transformation initiates at lath boundaries. We observe that both phase transformations are martensitic in nature and also occur at the same pressure, i.e. little hysteresis. The transformation start pressures and the kinetics of the transformation predicted by our model are in good agreement with experimental results.

Phase-field modeling of the beta to omega phase transformation in Zr–Nb alloys

A three-dimensional elastoplastic phase-field model is developed, using the finite element method (FEM), for modeling the athermal beta to omega phase transformation in Zr–Nb alloys by including plastic deformation and strain hardening of the material. The microstructure evolution during athermal transformation as well as under different stress states, e.g. uni-axial tensile and compressive, bi-axial tensile and compressive, shear and tri-axial loadings, is studied. The effects of plasticity, stress states and the stress loading direction on the microstructure evolution as well as on the mechanical properties are studied. The input data corresponding to a Zr – 8 at% Nb alloy are acquired from experimental studies as well as by using the CALPHAD method. Our simulations show that the four different omega variants grow as ellipsoidal shaped particles. Our results show that due to stress relaxation, the athermal phase transformation occurs slightly more readily in the presence of plasticity compared to that in its absence. The evolution of omega phase is different under different stress states, which leads to the differences in the mechanical properties of the material. The variant selection mechanism, i.e. formation of different variants under different stress loading directions, is also nicely captured by our model.

Optimization of Mo Content in Beta-Type Ti-Mo Alloys for Obtaining Larger Changeable Young’s Modulus during Deformation for Use in Spinal Fixation Applications

In order to meet the requirements of the patients and surgeons simultaneously for spinal fixation applications, beta (β) -type Ti-Mo alloys with self-tunable Young’s modulus due to deformation have been developed to prevent the stress-shielding effect for patients and to suppress springback for surgeons. In this study, the effects of Mo on the deformation-induced omega-phase transformation were investigated and then the Mo content in binary Ti-Mo alloys was optimized in order to achieve a large increase in Young’s modulus via deformation-induced omega-phase transformation, leading to suppression of springback.

Texture in two cold-drawn beta Ti alloys

Synchrotron X-ray diffraction was used to measure the textures in two heavily cold-drawn beta Ti alloys (i.e. beta III Ti alloy and Ti–15Mo alloy). Instead of the well-known β texture, the β texture was found in the cold-drawn condition along with a strong ω texture. The cause of the texture in the β phase is possibly related to the stress-induced omega phase transformation during the cold-drawing process.

Electronically driven instabilities in metals

Electronically driven instabilities of the conduction electrons in metals are manifested as spin density waves, charge density waves accompanied by periodic lattice distortions, or in structural phase transformations and are thought to result from a divergence in X(q). the generalized static electronic susceptibility. Examples of these instabilities are discussed by means of accurate calculations of the noninteraction conduction electron susceptibility X(q) using results of energy-band calculations and our recently developed analytic tetrahedron linear energy method, notably, the occurrence of change density waves in the layered dichalcogenides and the body-centered cubic to omega phase transformation in metals like Zr.

The influence of shock prestraining on the structure/property response of hafnium

Highly-textured, crystal-bar-purity hafnium has been shock prestrained at 4.96 and 11 GPa, below the reported alpha to omega phase transformation of 38 GPa. The specimens were soft caught following shock prestraining to facilitate quantification of the substructure and post shock constitutive behavior. The substructure of the shocked materials was investigated using optical and transmission electron microscopy. The preshocked Hf samples were subsequently reloaded quasi-statically in compression. The deformation behavior of the as-annealed hafnium under quasi-static conditions is compared to its response following shock prestraining. The reload response is correlated to differences in the defect density due to shock loading.

Nucleation of athermal omega phase in Cu–Zn system

Nucleation of the athermal omega (ω) phase transformation in the body-centered cubic parent phase is studied by evaluating the reciprocal free energy which includes the properties of coherent strain energy and the bulk free energy change. The droplet model of the omega formation is combined with the Landau-type of the free energy expression of phase transformation. The metastable ω cluster having a two dimensionally expanded dual phase structure is suggested to form in the heterophase fluctuation. Quantitative calculation of free energy has identified the critical transformation temperature T 0 = 300 K in β-brass that is defined as the temperature at which the free energy of the metastable phase is the same as the free energy of the parent phase. The continuous transformation from the metastable ω cluster to a stable ω phase is shown to occur at the transformation temperature T ω that is well below T 0.

The influence of oxygen content on the α to ω phase transformation and shock hardening of titanium

In this study the influence of alloy chemistry on the propensity of omega phase formation in two titanium alloys during shock loading is examined. The effect of peak shock stress on the phase stability and substructural evolution of high purity and A-70 (3700ppm oxygen) titanium was probed utilizing velocity interferometer system for any reflector and post shock substructural analysis. While in the high purity titanium the alpha to omega phase transformation was found to occur at 10.4GPa, no transformation was observed in the A-70 material for stresses up to 35GPa. Transmission electron microscopy analysis and neutron diffraction of shock-recovered samples confirmed these results and probed the details of twin and dislocation structures. Debye temperature data are also presented and the Debye-Waller temperatures for the alpha and omega phases in the high purity titanium are calculated. Finally, the compressive, quasistatic reload behaviors of both high purity and A-70 titanium are compared to the as-annealed counterparts at comparable strains and discussed in terms of the phase transformation and the shock-induced defect generation.

Beta to Omega Phase Transformation in a Ti-Mo Alloy Deformed in an Impact Compression Mode Due to Aging

Beta to Omega Phase Transformation in a Ti-Mo Alloy Deformed in an Impact Compression Mode Due to Aging

Simple models for the omega phase transformation

In the late sixties, it was recognized that the omega phase transformation occurring in bcc Ti, Zr, and Hf alloys was a displacive transition which could be described, at least qualitatively, by simple models. Since the displacive wave responsible for the transition to perfect omega was a Brillouin zone boundary wave, displacements and volume changes were rather small, in contrast to the classical martensite case. The nonideal, or modulated omega phase requires further consideration, and calls for soliton models, for example. Recent first principles electronic structure calculations, briefly reported upon here, have also shed light on the athermal omega transformation.

The structure of a linear omega-like vacancy defect in Zr-Nb B.C.C. solid solutions

Many Ti and Zr-base alloy systems in which a metastabile structure called the omega phase is formed, exhibit a characteristic diffuse scattering distribution from the untransformed b.c.c. solid solution. These diffuse scattering observations indicate that a localized defect is present in the b.c.c. solid solution. In the present work the structure of a new type of defect in the b.c.c. phase was determined using published diffuse scattering observations for a Zr-20 wt % Nb alloy. The defect was shown to consist of a vacancy about which are rows of atoms displaced along one 〈111〉 direction. The particular 〈111〉 displacements that occur on opposite sides of the vacancy give rise to structures that are similar to two subvariants of the omega phase. This sequence of subvariants and the additional small displacements normal to the 〈111〉 direction can explain the observed diffuse peak shifts characteristic of many Ti and Zr alloy systems. On the basis of the diffraction analysis alone it is not possible to state that the defect structure arrived at is unique. However, this structure does provide the best fit to the observations of all the models tried, and it explains in a physically reasonable manner many of the details of the diffuse scattering. The similarity of this new defect to the omega phase, suggests that it plays an important role in the mechanism of the omega phase transformation. What this role is, still remains to be determined.

A high resolution electron microscope study of the omega transformation in ZrNb alloys

High resolution direct lattice imaging and dark field electron microscopl lere used to examine the omega phase transformation in lr-Nb allols. Direct lattice imaging demonstrated the existence of subvariants lithin an omega variant. The existence of an ordered sequence of subvariants, lhich is the basic premise of recent diffuse intensitl calculations lhich seek to explain diffuse diffraction observations in high Nb content allols, could not be checked because of the small sile of the omega regions. In the lol Nb content allols dark field electron microscopl was used to shol that the λ phase consists of large domains (100–200 Å dia.) the interior of lhich contains features that are 3–6 Å dia. As the Nb content is increased the omega domains decrease in sile until onll 3–5 Å images are observed in allols containing 15lt.% Nb or more. The isolated images are present over the range of composition from 8 to 30lt.% Nb. Time sequence dark field micrographs shol that these small images change lith time. The diffuse λ reflections are believed due in part to the existence of a 〈111〉 linear detect, consisting of groups of 〈111〉 rols of atoms lhich are displaced from b.c.c. to λ positions for short periods of time.

The Stress-induced omega phase transformation in Ti-V alloys

The deformation behavior of bcc (β) Ti-V single crystals containing the athermal ω phase was studied using tensile tests, optical and electron microscopy and X-ray and electron diffraction. The stress-strain curves were characterized by a marked yield point and an essentially zero work hardening rate. The deformation structures consisted of wavy slip and stress-induced plates. Both X-ray and electron diffraction showed that the stress-induced plates consist of one variant of the omega phase, with the orientation relation to the parents phase close to (0001)ω ‖(001)ω; (•1120)ω ‖(110)β. The habit plane was of the type 554. A small amount of ά (hcp) phase was present within the ω plate, with orientation relation to the β phase close to the Burgers relationshipi.e. (0001)ά, ‖(110)β; [•1120]ά ‖[•111]β. It is suggested that the ω phase may be an intermediate structure in the stress-induced bcc → hep transformation.